Oden guided the Buckeyes to the NCAA championship game last season before they were knocked off by the Florida Gators -- a team that had three of their players chosen in the first nine picks.
Five international players went in the first round, led by Yi Jianlian of China. Yi was chosen sixth by Milwaukee. Players from Italy, Spain, Brazil and Finland were also first-round choices.
Oden, who averaged 15.7 points a game last season, joins a team that went 32-50 during the 2006-07 campaign and missed the playoffs for the fourth straight year.
Seattle, picking in the second spot, chose Texas forward Kevin Durant. Forward Al Horford of Florida went third to Atlanta, followed by guard Mike Conley of Ohio State to Memphis and forward Jeff Green of Georgetown to Boston. Green was later traded to Seattle.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes